Old barbarian — cause of complaint — leading demo (6,5)
I believe the answer is:
Here is my best explanation:
'demo' is the definition.
'old barbarian cause of complaint leading' is the subsidiary indication.
'old barbarian' becomes 'hun'.
'cause of complaint' becomes 'germ' (might cause a medical complaint).
'leading' becomes 'arch' (e.g. in arch-enemy).
(Other definitions for hunger march that I've seen before include "movement that brings protest" and "1936 Jarrow demonstration".)